How do I transfer only single vertex groups between objects?
Select object where you'd like the vertex group to copy to. You don't need to create empty vertex group there as it will be added automatically, still it's possible to do for testing purposes.
With this object still selected,  Shift + RMB to select object which has original vertex group.
Choose Copy Vertex Group entry from drop-down menu. The thing is that you should select mesh with vertex group to be copied last.